On the trace of an idempotent in a group ring
On the trace of an idempotent in a group ring
Let <italic>KG</italic> be the group ring of a polycyclic by finite group <italic>G</italic> over a field <italic>K</italic> of characteristic zero. It is proved that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="e equals sigma-summation e left-parenthesis g right-parenthesis g"> <mml:semantics> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>=</mml:mo> <mml:mo>∑<!-- ∑ --></mml:mo> <mml:mi>e</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy="false">)</mml:mo> …